SOLUTION: I have a word problem and not sure how to set up the equation: A furniture company needs to ship 96 sofas and 57 chairs They have small trucks and large trucks Each small truc

Question 118038: I have a word problem and not sure how to set up the equation:
A furniture company needs to ship 96 sofas and 57 chairs
They have small trucks and large trucks
Each small truck is designed to hold 4 sofas and 3 chairs
Each large truck is designed to hold 12 sofas and 6 chairs
Let x represent the number of small trucks needed
Let y represent the number of large trucks needs.
Write the system of equatin that represents this situation then solve.
So far I have x=4a+3b
y=12a+6b
Am I even on the right track? I am the worst at word problems and this one seems to have me stumped. Any help is greatly appreciated.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
I have a word problem and not sure how to set up the equation:
A furniture company needs to ship 96 sofas and 57 chairs
They have small trucks and large trucks
Each small truck is designed to hold 4 sofas and 3 chairs
Each large truck is designed to hold 12 sofas and 6 chairs
Let x represent the number of small trucks needed
Let y represent the number of large trucks needs.
Write the system of equation that represents this situation then solve.
:
Sofa equation
4x + 12y = 96
:
Chair equation
3x + 6y = 57
:
Solve by elimination: Multiply the chair equation by 2, subtract sofa equation
6x + 12y = 114
4x + 12y = 96
---------------subtracting eliminates y, solve for x
2x + 0y = 18
x = 18/2
x = 9 small trucks
:
Find y
using sofa equation, substitute 9 for x
4(9) + 12y = 96
36 + 12y = 96
12y = 96 - 36
12y = 60
y = 60/12
y = 5 large trucks
:
Check solutions in the chair equation:
3(9) + 6(5) =
27 + 30 = 57 as required
:
Hope this helped & Merry Christmas!!

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